Filtration in porous media of fluids and gases containing associated with them (dissolved, particulate) solid substances is accompanied by the diffusion of these substances and mass transfer between the liquid (gas) and solid stages. The most common types of mass transfer are sorption and desorption, ion exchange, dissolution and crystallization, mudding, sulfation and suffusion, waxing. We consider the system of equations modeling the process of non-equilibrium sorption. We formulate a difference approximation of the differential problem by an implicit scheme. The solution to the difference problem is constructed by the sweep method. Basing on the numerical results, we can conclude the following: as the relaxation time decreases, the solution to the non-equilibrium problem tends to the solution of the equilibrium problem as the time increases.

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In this paper, we investigated a two-phase model of incompressible fluid filtration. We apply the irregular grid method and the variable direction scheme. This approach gives the effect of solution accuracy near discontinuities (wells) due to the use of an irregular grid. The model is built taking into account the influence of capillary pressure and gravitational forces. The results confirm that the amount of oil that came out of the layer in a certain time is equal to the volume of water injected, except for the amount of water in the outlet stream in the same time. The proposed solutions of the new approach are intended to improve the methods and schemes of numerical investigation of this model. A balanced monotonic finitedifference scheme was developed and an efficient algorithm for its implementation was proposed. From a practical point of view, numerical modeling allows early prediction of performance. Thus, the applied aspect of the use of the obtained scientific result is the possibility of improving the process by taking into account the distribution of water saturation in the layer.

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